LCM of 72, 108 and 2100 is 37800. LCM is the number which is divisible by 72, 108 and 2100 evenly. Among the common multiples, the least common multiple of 72, 108 and 2100 can be found. The multiples of 72 are (72, 144, 216, 288, 360, ….), the multiples of 108 are (108, 216, 324, 432, 540, ….) and the multiples of 2100 are (2100, 4200, 6300, 8400, 10500, ….) respectively. Division, Prime factorisation and listing of the multiples are the common methods used to find the LCM value.
Also read: Least common multiple
What is LCM of 72, 108 and 2100?
The answer to this question is 37800. The LCM of 72, 108 and 2100 using various methods is shown in this article for your reference. The LCM of two non-zero integers, 72, 108 and 2100, is the smallest positive integer 37800 which is divisible by both 72, 108 and 2100 with no remainder.
How to Find LCM of 72, 108 and 2100?
LCM of 72, 108 and 2100 can be found using three methods:
- Prime Factorisation
- Division method
- Listing the multiples
LCM of 72, 108 and 2100 Using Prime Factorisation Method
The prime factorisation of 72, 108 and 2100, respectively, is given by:
72 = 2 x 2 x 2 x 3 x 3 = 2³ x 3²
108 = 2 x 2 x 3 x 3 x 3 = 2² x 3³
2100 = 2 x 2 x 3 x 5 x 5 x 7 = 2² x 3¹ x 5² x 7¹
LCM (72, 108, 2100) = 37800
LCM of 72, 108 and 2100 Using Division Method
We’ll divide the numbers (72, 108, 2100) by their prime factors to get the LCM of 72, 108 and 2100 using the division method (preferably common). The LCM of 72, 108 and 2100 is calculated by multiplying these divisors.
|
2 |
72 |
108 |
2100 |
|
2 |
36 |
54 |
1050 |
|
2 |
18 |
27 |
525 |
|
3 |
9 |
27 |
525 |
|
3 |
3 |
9 |
175 |
|
3 |
1 |
3 |
175 |
|
5 |
1 |
1 |
175 |
|
5 |
1 |
1 |
35 |
|
7 |
1 |
1 |
7 |
|
x |
1 |
1 |
1 |
No further division can be done.
Hence, LCM (72, 108, 2100) = 37800
LCM of 72, 108 and 2100 Using Listing the Multiples
To calculate the LCM of 72, 108 and 2100 by listing out the common multiples, list the multiples as shown below
Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, . . . ., 37656, 37728, 37800, . . . .
Multiples of 108 = 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, . . . ., 37476, 37584, 37692, 37800, . . . .
Multiples of 2100 = 2100, 4200, 6300, 8400, 10500, 12600, 14700, 16800, 18900, 21000, . . . ., 29400, 31500, 33600, 35700, 37800, . . . .
LCM (72, 108, 2100) = 37800
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LCM of 72, 108 and 2100 Solved Examples
Question: What is the smallest number which is exactly divisible by 72, 108 and 2100?
Solution:
The LCM of 72, 108 and 2100 is the smallest number exactly divisible by the given numbers.
Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, . . . ., 37656, 37728, 37800, . . . .
Multiples of 108 = 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, . . . ., 37476, 37584, 37692, 37800, . . . .
Multiples of 2100 = 2100, 4200, 6300, 8400, 10500, 12600, 14700, 16800, 18900, 21000, . . . ., 29400, 31500, 33600, 35700, 37800, . . . .
Hence, the LCM is 37800.
Frequently Asked Questions on LCM of 72, 108 and 2100
What is the LCM of 72, 108 and 2100?
We know that,
Multiples of 72 = 72, 144, 216, 288, 360, 432, 504, 576, 648, 720, . . . ., 37656, 37728, 37800, . . . .
Multiples of 108 = 108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, . . . ., 37476, 37584, 37692, 37800, . . . .
Multiples of 2100 = 2100, 4200, 6300, 8400, 10500, 12600, 14700, 16800, 18900, 21000, . . . ., 29400, 31500, 33600, 35700, 37800, . . . .
The smallest multiple exactly divisible by 72, 108 and 2100 is 37800.
If the LCM of 72, 108 and 2100 is 37800, determine the GCF.
LCM x GCF = 72 x 108 x 2100
Given,
LCM of 72, 108 and 2100 is 37800
37800 x GCF = 16329600
GCF = 16329600/37800 = 432
Write the methods used to find the LCM of 72, 108 and 2100.
The methods used to find the LCM of 72, 108 and 2100 are
Division method
Prime Factorisation
Listing the multiples
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